半平面下含內嵌物之裂紋彈動行為之研究

Eastodynamic Response of a Sub-Crack with an Inserted Material in a Half-Plane Medium

10.6607/BTSU.2010.1.8

翁燈景(D.C Wong)；盧炳志(P.C. Lu)李冠霈(K.P. Lee)

散射 ； 邊界積分法 ； 應力強度因子 ； scattering ； BIM ； stress intensity factor

台灣首府大學學報

1期（2010 / 09 / 01）

167 - 187

繁體中文

本文旨在探討二維半無限域彈性體內，彈性波與裂紋交互作用之暫態散射情形。問題中之裂紋具有任意傾斜角度、任意垂直距離（離自由表面）且內含有異質物，而裂紋內之異質物則以含有集中質量之線性彈簧模式模擬。本文所考慮的彈性波有P波、SV波及表面波等。分析方法乃利用Fourier轉換將時域散射問題轉為頻率域散射問題。在頻率域內利用邊界元素法配合問題之邊界條件求得頻率域之穩態解。而最後利用快速Fourier反變換求得時間域之暫態解。本文之數值結果將以頻率域及時間域兩方面之自由表面位移、裂紋尖端動態應力強度因子及裂紋開口位移等物理量表達，並就異質物之勁度大小、裂紋之傾斜角度、垂直距離及入射波之入射角度對這些物理量的影響進行討論。此些分析結果除了可應用於焊接構件之破壞力學設計上之外，並可應用於超音波非破壞評估方面。

The scattering problem of elastic waves by a sub-crack with the inserted material, arbitrary angle and vertical distance from the free boundary of an elastic half-plane medium was investigated in frequency as well as in time domains. A spring model is used to model the stiffness of the inserted material, and the inertial effect was also considered. The incident waves considered here were P, SV and Rayleigh waves. The displacement boundary integral equation (DBIE) and the traction boundary integral equation (TBIE) are first formulated in frequency domain. Then employing the boundary element method with appropriate boundary conditions, the DBIE and TBIE can be solved numerically. Finally, the transient response due to a step stress pulse was evaluated by using inversed FFT. Numerical calculations are accomplished for following physical quantities: the displacements on the free boundary of half-plan, the crack opening displacements and the dynamic stress intensity factors. The effect of mass and stiffness of the inserted material, inclined angles and vertical distances of the crack and the angles of incident elastic waves to those quantities also were analyzed and discussed.